Time-periodic laminar mixed convection in an inclined channel

The steady-periodic regime of laminar mixed convection in an inclined channel is studied analytically, with the following boundary conditions: the temperature of one channel wall is stationary, while the temperature of the other wall is a sinusoidal function of time. Analytical expressions of the velocity field, of the temperature field, of the pressure drop, of the friction factors, as well as of the Nusselt number at any plane parallel to the walls are determined. It is found that, for every value of the Prandtl number greater than 0.277, there exists a resonance frequency which maximizes the amplitude of the friction factor oscillations at the unsteady-temperature wall. Moreover, for any plane which lies between the midplane of the channel and the unsteady-temperature wall, every value of the Prandtl number yields a resonance frequency which maximizes the amplitude of the Nusselt number oscillations.